Pub. Date:
Cambridge University Press
Results and Problems in Combinatorial Geometry

Results and Problems in Combinatorial Geometry


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In this short book, the authors discuss three types of problems from combinatorial geometry: Borsuk's partition problem, covering convex bodies by smaller homothetic bodies, and the illumination problem. They show how closely related these problems are to each other. The presentation is elementary, with no more than high-school mathematics and an interest in geometry required to follow the arguments. Most of the discussion is restricted to two- and three-dimensional Euclidean space, though sometimes more general results and problems are given. Thus even the mathematically unsophisticated reader can grasp some of the results of a branch of twentieth-century mathematics that has applications in such disciplines as mathematical programming, operations research and theoretical computer science. At the end of the book the authors have collected together a set of unsolved and partially solved problems that a sixth-form student should be able to understand and even attempt to solve.

Product Details

ISBN-13: 9780521269230
Publisher: Cambridge University Press
Publication date: 10/10/1985
Pages: 120
Product dimensions: 5.43(w) x 8.50(h) x 0.28(d)

Table of Contents

1. Partition of a set into sets of smaller diameter; 2. The covering of convex bodies with homothetic bodies and the illumination problem; 3. Some related problems.

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